The Capita run firm has admitted the error, which the Mail understands happened just before last weekend, and has now made refunds to all involved.

But some refunds could take several days to clear through the banks at a time of year when many accounts are at a post Christmas low.

The Mail understands that anyone incurring bank charges for being overdrawn as a result of the error will be compensated.

A spokeswoman for Service Birmingham, which collects the council tax in the city, said: “Due to a processing error, 3,447 duplicate transactions were made for payments to Birmingham City Council.

“All affected people and organisations were informed of the error, and refunds were made.

‘‘We would like to apologise to those affected and reassure them that we have taken steps to mitigate the risk of this happening again.”

But one Mail reader said: “I have just checked my bank account only to find they have taken my debit card payment twice. I rang them up to complain and was told computer error has hit many people and they will return the money in a few days.

“What happens to people who cannot be without of hundreds of pounds for a few days?”

Birmingham City Council handed over its council tax collection department to Capita Service Birmingham in 2011 with a commitment to raise collection rates from 96.3 per cent to 98 per cent - insuring an extra £4.8 million income for the local authority.

It was part of the deal which saw the controversial IT contract with the company extended by five years until the end of the decade.